Question

Consider the bonding in an \(\mathrm{MgH}_{2}\) molecule. (a) Draw a Lewis structure for the molecule, and predict its molecular geometry. (b) What hybridization scheme is used in \(\mathrm{MgH}_{2}\) ? (c) Sketch one of the two-electron bonds between an \(\mathrm{Mg}\) hybrid orbital and an \(\mathrm{H} 1 \mathrm{~s}\) atomic orbital.

Short answer

The Lewis structure for MgH2 is H-Mg-H with a linear molecular geometry. The hybridization scheme used is sp, where Mg hybridizes its 3s and one of the 3p orbitals to form two sp hybrid orbitals. One of the two-electron bonds between an Mg hybrid orbital and an H 1s atomic orbital is formed by the overlap of an Mg sp hybrid orbital and an H 1s atomic orbital, with maximum electron density between the two nuclei.

Step-by-step solution

1. Draw the Lewis structure for MgH2

To draw the Lewis structure for MgH2, first, count the total number of valence electrons. Magnesium (Mg) has 2 valence electrons, and each hydrogen (H) atom has 1 valence electron, which gives a total of 4 valence electrons. Now place the Mg atom in the center and the H atoms on either side of it. Then, connect the H atoms to the Mg atom using single bonds. Since Mg has 2 valence electrons and each H atom needs 1 electron to complete its valence shell, the electrons are shared in a way that every atom has a complete valence shell. The Lewis structure for MgH2 is: ``` H - Mg - H ```

2. Predict the molecular geometry of MgH2

To predict the molecular geometry of MgH2, we use the VSEPR (Valence Shell Electron Pair Repulsion) theory, which states that the electron pairs around a central atom repel each other and adopt a geometry that minimizes the repulsion between these electron pairs. In MgH2, there are no lone pairs on the Mg atom, and it is bonded to two H atoms. The electron pairs are spread out as far apart as possible to minimize repulsion, resulting in a linear molecular geometry.

3. Determine the hybridization scheme used in MgH2

To determine the hybridization scheme in MgH2, first, identify the electron-domain geometry around the central atom, Mg. There are two regions of electron density around Mg due to its bonding with two H atoms, which gives an electron-domain geometry of linear. For a linear electron-domain geometry, the hybridization scheme is sp. This means that the central atom, Mg, hybridizes its 3s and one of the 3p orbitals to form two sp hybrid orbitals.

4. Sketch one of the two-electron bonds between an Mg hybrid orbital and an H 1s atomic orbital

To sketch one of the two-electron bonds between an Mg hybrid orbital and an H 1s atomic orbital, start by drawing the Mg atom with its two sp hybrid orbitals. One of the sp orbitals points toward one H atom, and the other sp orbital points in the opposite direction toward the other H atom. Now, draw an H 1s atomic orbital overlapping with one of the Mg sp hybrid orbitals, where the electron density is maximum between the two nuclei, forming a bond. The electron sharing between the Mg sp hybrid orbital and the H 1s atomic orbital results in the formation of a two-electron bond, allowing both atoms to complete their valence shells.

Key concepts

Lewis Structure of MgH2

Understanding the Lewis structure of MgH2 is pivotal in grasping the molecule's bonding. It allows us to visualize the distribution of valence electrons among the atoms. Magnesium has two valence electrons, while each hydrogen atom has one. By pairing the hydrogen atoms with magnesium, we create single bonds satisfying the full valence shell for hydrogen.

In the Lewis structure, magnesium is positioned in the center with one hydrogen atom bonded to each side. The structure takes the form:

• H—Mg—H

Each hydrogen now has a complete shell with 2 electrons. Magnesium, initially with 2 valence electrons, has shared these with two hydrogen atoms, thus achieving a stable structure.

VSEPR Theory

VSEPR theory, or Valence Shell Electron Pair Repulsion theory, imparts a powerful method to predict the molecular geometry of a molecule. This theory posits that electron pairs around a central atom will orient themselves as far apart as possible to minimize repulsion. In MgH2, magnesium is the central atom with no lone pairs, only bonded pairs.

The absence of lone pairs means that the electron pairs associated with the H atoms will push away from each other, as is their natural tendency according to VSEPR. With only two bonding electron pairs, they will repel and arrange themselves opposite each other, making the molecule linear.

sp Hybridization

The concept of hybridization provides a deeper explanation of the molecular bonding in MgH2. The linear geometry of MgH2 implies that the central magnesium atom undergoes sp hybridization. This process involves the mixing of one s and one p orbital from the magnesium atom to form two equivalent sp hybrid orbitals.

These two sp orbitals are arranged linearly, 180 degrees apart, which aligns perfectly with the hydrogen atoms. This permits the formation of two strong, covalent bonds between the magnesium and the hydrogen atoms. The sp hybridization of MgH2 is an intrinsic characteristic that explains the bonding angle and strength between the atoms.

Molecular Geometry Prediction

Predicting molecular geometry is pivotal for understanding the physical and chemical properties of compounds. In the case of MgH2, both VSEPR theory and hybridization can be utilized for prediction. With sp hybridization and no lone pairs to consider, VSEPR theory anticipates a linear arrangement.

This prediction aligns with what we observe for the MgH2 molecule. The linear geometry of MgH2 has implications that range from its reactivity to its physical attributes. By combining our understanding of the Lewis structure, VSEPR theory, and hybridization, we gain a multi-faceted view of the structural characteristics of MgH2.